Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T05:45:00.651Z Has data issue: false hasContentIssue false

Wreath Powers and Characteristically Simple Groups

Published online by Cambridge University Press:  24 October 2008

P. Hall
Affiliation:
King's CollegeCambridge

Extract

A group G is called characteristically simple if it has no characteristic subgroups other than itself and the unit subgroup. For brevity, we call such groups -groups; we also use to denote the class of all characteristically simple groups.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1962

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)McLain, D. HA characteristically-simple group. Proc. Cambridge Philos. Soc. 50 (1954), 641642.CrossRefGoogle Scholar
(2)Baer, R.Über Nil-Gruppen. Math. Z. 62 (1955), 402437.CrossRefGoogle Scholar
(3)Kaloujnine, L.La structure des p−groupes de Sylow des groupes symmétriques finis. Ann. Sci. École Norm. Sup. 65 (1948), 239276.CrossRefGoogle Scholar
(4)Hall, P.The Frattini subgroups of finitely generated groups. Proc. London Math. Soc. (3), 11 (1961), 327352.CrossRefGoogle Scholar
(5)Kurosh, A. GThe theory of groups, vol. II (Chelsea; New York, 1956).Google Scholar
(6)McLain, D. HFiniteness conditions in locally soluble groups. J. London Math. Soc. 34 (1959), 101107.CrossRefGoogle Scholar
(7)Gruenberg, K.The Engel elements of a soluble group. Illinois J. Math. 3 (1959), 151167.CrossRefGoogle Scholar
(8)Neumann, B. H.Ascending derived series. Compoailio Math. 13 (1956), 4764, andGoogle Scholar
Ascending derived series. Compoailio Math. 128.Google Scholar
(9)Hall, P.Some constructions for locally finite groups. J. London Math. Soc. 34 (1959), 305319.CrossRefGoogle Scholar
(10)Ore, O.Theory of monomial groups. Trans. American Math. Soc. 51 (1942), 1564.CrossRefGoogle Scholar
(11)Lazard, M.Sur les groupes nilpotents et les anneaux de Lie. Ann. Sci. École Norm. Sup. 71 (1954), 101190.CrossRefGoogle Scholar
(12)Kaloujnine, L. and Krasner, M.Produit complet des groupes de permutations et probleme d'extension des groupes. Acta Sci. Math. Szeged, 13 (1950), 208230; 14 (1951), 39–66 and 69–82.Google Scholar
(13)Hall, P.Some sufficient conditions for a group to be nilpotent. Illinois J. Math. 2 (1958), 787801.CrossRefGoogle Scholar
(14)Cohn, P. MGroups of order-automorphisms of ordered sets. Mathematika, 4 (1957), 4150.CrossRefGoogle Scholar
(15)Livčak, YA. B.A locally soluble group which is not an SN*-group. Dokl. Akad. Nauk SSSR, 125 (1959), 266268. (In Russian.)Google Scholar